A Sudoku With Only 1 Given Digit?!

Added: 2026-06-03

[00:00:14]Hello and welcome to Wednesday's edition of Cracking the Cryptic, where we've got a treat for you today. A treat because we can't do Rat Run today. Uh, the last gazillion Wednesdays have been taken up with Marty Sears's incredible Rat Run series. But the f the day new of the whole of Rat Run ever, I think is next Tuesday. Um, which means that this Wednesday, we have to find something else to do. And who better to substitute in for Marty than the incredible Dutch Grandmaster Ard Van Deering with one of his puzzles called 24 squares. um which which features an an absolutely typical Odd rule set. Art's puzzles are they are amazing. He is responsible for some of our most popular videos because his puzzles are just they have something that captivates everybody who tries them. Um and I think our biggest ever video has had over 10 million views. I know that. And that's definitely an odd odd puzzle. The Sudoku with only four given digits, but he's he's over 80 now.

[00:01:19]Art is and he's still on a weekly basis sending us incredible original puzzles always with short rule sets. Um I have to confess now we r very rarely get Arts puzzles tested because we know who Art is. Art is a genius. Um so I don't know how difficult this one is. It's not being tested. Um Mark's put it into the software for me. I don't know whether he's had a go at it or not. Um but basically we've got to fill these every line with square numbers. Um and they I mean I I will go through the rules properly but that's essentially it. And I'm guessing there are 24 24 such lines are there. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20.

[00:02:08]Yes, there are. There are 24. There's that one. That purple one sitting on the edge made me wonder whether that there were there was actually an odd number of squares but I think because that one is sort of it's symmetrical but it it's it's not got a symmetrical counterpart.

[00:02:22]Uh we are back on an even number of squares and there are indeed 24 and there is a given digit. Art is always art's always quite generous in modern Sedoku parliament. Um it's quite rare nowadays we get any given digits at all.

[00:02:36]Art normally gives us uh between about 1 and six, but today we get one. And I'll read you the rules and we'll have a go at this together in a moment or two's time. Um, what can I tell you about though before we kick off? Uh, let me just run through my my mental list over on Patreon with the US declassifying all of these uh files about aliens. We have of course got our Sudoku competition for the month of June themed around that de declassification and all of these um Sudokus that have appear seem to be appearing in these alien files. You you've all been enjoying it. All those of you who've had a go so far. So we're delighted to see that. Closing dates the 20th. So you've got plenty of time. If you'd like to win the chance to come on to the channel and solve a puzzle, do get involved in that. It's over on Patreon right now. Um, other big news of course is this new app that we've got out by the great Zetamath. Um, so we've got Zetamath's Worm, a series of linked Sedokus. Um, that's that's absolutely brilliant stuff. So do do check that out. You can um you can get that on wherever wherever you get your appses.

[00:03:47]Um, where's that word come from? That's like something Gollum would say. Hobbits. Um.

[00:03:54]Ah, no. Well, you know where where you get your apps from. That's where you can get your Zeta worm. So, ah, the App Store, not the Apps store. The App Store, Google Play, and um Steam. Go and find the Zeta Math um app over there, and you'll you'll be in for a treat. Um now, let me let me distract myself from thoughts of Gollum by moving swiftly on to birthdays. Casper, Casper, it's your birthday today. You're turning 15. I know this because I had a lovely email from your mom, Jill, claiming that the only thing you'd asked for for your birthday this year was a shout out on the channel. That is absolutely charming. Um, Casper, I know you're into all things puzzly. So, I hope that there are some puzzle related presents for you. Um, I hope you have a great birthday today and of course that the chocolate cake is very heavily iced.

[00:04:48]Next, James, it's your birthday today. I know this because your partner Molly wrote to me. Um, she told me that you're going to be in Center Parks for your birthday and that brought back some memories. I have to say I haven't been to Center Parks for many many decades actually. Um, I actually I actually met a girlfriend at Center Parks once.

[00:05:10]That's that is back in the dimistant past. Um, Elizabeth, if you're watching, um, I don't know if you you probably won't remember me at all, but um, yeah, I met I met I met a girl called Elizabeth in Center Parks. Now, what year would that have been? I don't even dare reveal it. It was a long time ago, James. Anyway, great things happen at Center Parks. I hope they happen to for you, too. And I hope you can find some chocolate cake there. Um, next, Travis.

[00:05:40]Travis, it's your birthday today. And I know this because your girlfriend Aniston wrote to me um telling me that you had introduced her to Sudoku. Well, I think that is great. I'm always delighted when I hear that people are sharing the news about this wonderful hobby. So, thank you for doing that. I know that you both watch now. So, thank you both for watching. And Travis, I hope you have a great birthday today.

[00:06:03]And I hope you find some very heavily iced chocolate cake. Now, shall we have a go at 24 squares and see what the great Arvand Devatoring has in store?

[00:06:13]The rules of this one are as follows. We have got normal sudoku rules applying.

[00:06:17]So, we're going to put the digits 1 to nine once each and every row, every column and every 3x3 box.

[00:06:25]Each line contains a square number reading from left to right or in the case of the line in row 3, column 1, from top to bottom.

[00:06:35]Okay, that's a very very peculiar rule.

[00:06:38]Um, E, oh, there's an example. EG, if row 8 column 7 was a two, so this was a two.

[00:06:46]I'm guessing this would be a five to make 25. Let's just check that's right.

[00:06:50]Then row 7, column 8 must be a five.

[00:06:54]Yeah, to give 25. 25 is the only square number I know that's two digits that begins with a two.

[00:07:01]Right. And then we've got as an aid memoir, the squares without zeros or repeated digits are. And then there's a whole list of squares.

[00:07:10]I mean, I'm not going to read them out, but there there are a lot of them going all the way up to 961. I guess that could go on that line, couldn't it? Most of the squares are two digits. I think it's only that one that's three digits.

[00:07:26]So anyway, we've got a big long list of squares. So, if you didn't know your square numbers up to a thousand, you don't need to. Um, do have a go. The way to play is to click the link under the video as usual. But now I get to play.

[00:07:39]Let's get cracking.

[00:07:44]What on earth do you do to start this?

[00:07:47]We use the given digit. That's going to knock out 64 and 49 from those ones.

[00:07:57]That one couldn't be 64 because the four would be in the second position.

[00:08:05]So what does that mean? Um so so the square numbers the square numbers that we could wholly put in this box.

[00:08:18]So ignoring this one are selectable from 16 25. I'm looking at this list on the side. 16 25 36.

[00:08:29]Oh, there aren't that many. 16 25 36 81.

[00:08:37]Okay. And we couldn't use 16 and 81 on different squares, could we? Because they both need the digit one in them.

[00:08:45]So, we can only to put that another way, we can only use one of 16 and 81. So we must be using 25 and 36 in uh in these cells. They must include a 25 and a 36.

[00:09:01]So the starting digits are going to be twos in those positions. So fives must be in a final position and 36 has the same property.

[00:09:15]And oh I see no this is fine. This is fine because now having concluded we needed to use 36. I could have used 16 and 36, couldn't I? I just realized instead of I focused in on 81 and 16 which share a digit. But but now because we can't use 16 because we need 36 to be a pair or 36 to be a square, we're going to have to use 81, which means that this is actually a 238 triple and these are actually a 156 triple.

[00:09:50]And the digits we haven't put in are seven and no, we can't put seven. Seven is can never end a square number.

[00:10:02]Right. So that's a seven and that must be nine and that must be four because 49 is the only square number that ends in nine that's two digits long. We've actually got digits already.

[00:10:18]I've just realized something two. Ah right.

[00:10:24]I shouldn't have started like this should I? I should have started by thinking about seven. I did not realize this. Seven, looking at the list uh that I've got here of two-digit numbers in the instructions, seven doesn't appear in a two-digit square at all. Every other digit does.

[00:10:41]So, I could immediately have written seven into this box if I'd realized that. I can immediately write seven into this box because this is the only digit that doesn't appear on a square.

[00:10:53]Seven. Oh, look at this. It's lovely.

[00:10:55]Seven. I can just put the sevens into the grid. Uh well nearly seven can't go on any any any line in this puzzle cannot contain a seven.

[00:11:08]So seven by sudoku where because we can ask where seven goes in the middle row now and given its given its positions in boxes four and six. It's got to be on this this middle line. Thank goodness there is a list of three cell or threedigit squares.

[00:11:28]So which ones can have seven on 576 is an option. 729 is an option. 784 Oh 784 won't work. 784 would clash with this one.

[00:11:43]So I think there are only two that will work and they are 576. Let's put this in. 5 7 6 or 7 2 9.

[00:11:58]Now I wonder if either of those cause these other twodigit squares in the row to go wrong.

[00:12:09]So 576 would mean we couldn't use 25 or 36 or 64.

[00:12:20]But we could use 16, 49, or 81. So we'd have to use a one on one of them. And then 49 would have to be used if this was 576.

[00:12:35]But if this was 729, then we're getting rid of 25 and 49.

[00:12:46]So, we've got 16, 36, 64, and 81. Oh, goodness. That feels much that feels much more complicated actually if this was 729.

[00:13:01]Um, okay. Let let me distract myself from that because that that felt difficult to that can't be a seven.

[00:13:07]Look, because that's apparently got to be six or nine according to the options.

[00:13:16]H. Okay. I'm not sure whether I can use this yet. Should we try and do something else? What about What about nine in this box? 9 has to be 9 has to be 49, doesn't it? There's no other way of using a nine in a two-digit square.

[00:13:35]Yeah. So, so nine will have to be at the end of one of the one of those lines. So, it has it's only got three positions it can be in, which means four has to be ah okay, hang on. Four can't be in that one. So, that one can't be nine.

[00:13:55]So if four has been locked into two places in box one and nine has been locked into two places now I mean goodness me this is actually not very easy is it?

[00:14:19]Okay nine in column one we could do we can at least pencil mark it. Nine can't begin a two-digit square. The nine can't be in those cells. And it can't be here because this can't be a four.

[00:14:35]That's right. Is it? That is right.

[00:14:38]Sorry, I was just checking that that couldn't be a four cuz I was thinking why can't that be a nine? But but actually the reason this can't be a four is the corollery of the nine in box one being in one of those which forces the four into one of those which means this can't be a four and therefore this can't be a nine. So it is it is correct to say nine is in one of those two cells.

[00:15:02]Oh dear. This is this is actually this is actually not that easy. I don't think I I'm not I haven't got a good enough grasp of twodigit squares let alone three-digit squares to be sure of which numbers are most restricted here.

[00:15:19]Um, so four, so 49.

[00:15:26]So four is now unavailable for the six that we're we're going to put in this box, aren't we? In in the sense that I can't use 64 as a number anymore.

[00:15:39]That can't be a six because that would be a four.

[00:15:44]So 36 must be oh the hang on let's just check no that would be a four as well.

[00:15:52]So six in this box is also a finishing number because 64 is impossible. So it's going to be 36 which means six is in one of those and three is in one of those.

[00:16:10]Now, that's not even true.

[00:16:20]I don't like that because I'd forgotten about 16.

[00:16:27]Well, no. No, that's still valid. It's just No, it's a little bit valid. It's a little bit valid. We can still ask where six goes in this box. It is still a valid question. It really can't be the start of a square that has a four underneath it.

[00:16:44]So, it is it is an end digit, but the first digit doesn't have to be three. It could be one. And I've missed that.

[00:16:57]Oh, that's tricky then.

[00:17:02]I'm almost wondering whether you have to you you could almost pencil mark the first digit of all of these crosses with 1 2 3 4 6 8 and the final digit was 65. You see the final digit on any square is six if it's a twodigit square is 5 61 or 9. I know or four h69.

[00:17:37]1 4 5 69. So it could it could be necessary to think about it in that way.

[00:17:48]But I don't know what what on earth am I meant to do here?

[00:17:57]Um, I I really am not sure.

[00:18:04]Well, I've got to come up with something. Um, what what are the other digits that are 50? You can't Okay, you can't start a square with the number five.

[00:18:17]So, again, it's the same sort of point in box one. Five is going to be in the same positions as six and nine. So they are a 569 triple, right? See, that's far from obvious for for me at least. So they're a 569 triple, which means two is in one of these cells along with ones and sixes. So 1 6 2 4 because we don't know whether the six is assoc uh hang on not six three sorry because we don't know whether the six is associated with 16 or 36 the two is definitely associated with 5 25 and the four is definitely associated with the 9.

[00:19:08]So, in this box, what? There's a digit we haven't pencil marked at all. And that is the digit eight.

[00:19:16]That's weird.

[00:19:20]Okay. Well, one of those is an eight, which means one of these is a Well, that's a terrible pencil mark, but one of those is a one.

[00:19:30]Yeah. Okay. But we can we can extensify that pencil marking if that's even a word because we know that the um we know that the other digit that will be at the starting digit in these two cells will be whatever is not used on the number ending in six. So it must be a 1 or a three. So these are from 138. And these digits the ending digits are therefore definitely a one cuz the because of the 81 that will be required and then either and definitely a six because whether it starts with a one or a three we know the square number is always ending in six.

[00:20:10]So there is a one six pair now.

[00:20:13]Oh, I see if that was a six, I would know. I would know that one wasn't 576.

[00:20:20]But there there is a one six pair in row in row four. Now, okay, where's five in column one is a valid question because what we learned when we thought about it was that five can never start a square. So, five can't be in those, can't be in any of these.

[00:20:41]now. So, that is a 59 pair, which feels like it might do something.

[00:20:48]I don't think it's going to do anything in that row, but it could obviously Well, actually, whatever this was would determine this central uh this central three cell square.

[00:21:04]But I I think I'd rather look at row four to be honest because these are both Oh, no, that's a starting number. Oh, maybe I shouldn't. I don't I don't know what to look at.

[00:21:14]Okay, let's think about this cell.

[00:21:15]That's the starting number of the square. So, it could be a two with a five. It could be a three with a six.

[00:21:27]I think it could be. Can't be a four.

[00:21:30]Can't be a five. That starts no squares.

[00:21:33]Six. It can't be because there's a six in one of these. Seven starts no squares. Eight with a one would be the other alternative.

[00:21:47]And you sort of look along here and you think, can we find anything clever? I I maybe there's something, but I don't see what it is.

[00:21:59]Bobbins. Um, bobbins is the statement we're after.

[00:22:05]Okay. Okay. Now this digit on the other hand is the end of a square and the squares the two-digit squares end with a a peculiar cornucopia of digits. 1 4 5 69.

[00:22:20]So 14. So it's f Oh, don't tell me that's a five. That can't be true.

[00:22:27]I think it's a naked single. I don't trust this at all. 1 4 5 6 9. that. So yeah, if we fully pencil mark that, it's one of those options. It now sees a one six pair. It sees a four and it sees a nine in it column. I mean, that's just impossible. So this is a five. That's a two to make 25.

[00:22:49]That's now not a two. So that's not a five.

[00:22:58]So two in two in box one is now in one of these cells.

[00:23:06]Ah, hang on. Oh, nearly. I was nearly a good thought. I was going to say two is quite tricky then in box seven because two can't end a square number, can it?

[00:23:17]That's what we've just learned here. So, if two can't begin a square number and it can't ever end a square number, that could be a two as well. bother two is in one of those three positions which I don't think is going to help us.

[00:23:36]I'm afraid that's jolly annoying.

[00:23:43]It it probably column 7 we're meant to look at, isn't it?

[00:23:48]What do you think?

[00:23:50]Let's check these digits out because we know that four and nine were valid enders for um for this game we're playing. Um actually five is a valid ender as well with 25.

[00:24:05]So these two digits have to either be six like a number like 36 or one. Are they a one six pair?

[00:24:15]5 9. Yeah. So this is a one six pair.

[00:24:21]So these are going to be 81 or 36 or 16.

[00:24:34]16 feels impossible, aren't I? I'm going to get troubles with that, aren't I?

[00:24:38]Yeah. Uh yeah, 16 doesn't work because because imagine this is a one. Then this has to be a six to make 16. So that's a one as well. That's just doesn't work.

[00:24:50]That's very strange, but it doesn't work. So this is 38 and this is one six.

[00:24:59]So in in column seven now it's twos, threes, and eights. I mean, how does art come up with this stuff? It's just bizarre, isn't it?

[00:25:08]This can't be a two because that would require a five here. So this one's three or eight. So this is either six or one.

[00:25:15]which means I've got a one six pair in box six out of nowhere and this is 2 three or eight. So that is 5 6 or 1. So now I've got a 56 triple in column 8.

[00:25:34]Okay. So what we should check is these two digits which commence squares.

[00:25:40]Now, we can have a 25, we can have a 36, we can have a 49, and we can have an 81.

[00:25:46]Oh dear.

[00:25:49]So, that didn't Well, oh, I see. Yeah. Okay. So, if you look at column 8, what we should have said, or what I should have said is where's nine? Cuz nine can never commence a square. So, there's been a seven N pair there, but donkeyy's ears probably. Um, so this box has got interesting, hasn't it? There's a 1 six pair, a 7 9 pair, and a five. So these digits are 2 3 4 8.

[00:26:21]But don't we know don't don't we know something about this row?

[00:26:31]Um, we probably do somehow.

[00:26:40]576 would push four into that cell.

[00:26:47]81.

[00:26:49]That doesn't work. That's really weird.

[00:26:54]I think if this is 576, this might end up being 23, which or 32, which won't work for a square. Let me just see if that I might be wrong about that. I'm just going to see if 729 gives any option at all. That would rule out 25.

[00:27:13]Sorry. So 7 729 would make this a five 81 36 and that could be a four, I think.

[00:27:25]Okay, I there's at least one way of working it with 729, but I don't think let let me just check that I'm right about this. If this is 576, that is the number, isn't it? 576. What I noticed about that is that this digit becomes a one, which means this will be an 8. So, we're going to have 1 8 9 in the row in these positions.

[00:27:49]And we the only I suppose the way to think about this now is to say this digit is 2 3 or four.

[00:27:56]Uh I was thinking about 49 not being a possible. So that's why I was putting the four here or 64. So but but but in effect what you can see is that these two digits here are selected from 2 3 and four and there's no possible square you can make. So at least we're going to get this um this central thing sorted out. It is 729.

[00:28:18]Whoa, whoa. 729.

[00:28:22]Now hope. So this is five. This is nine.

[00:28:25]This is nine. This is seven. So this is so we've actually getting some digits from this.

[00:28:32]So this is not two anymore.

[00:28:40]Um so what does all this mean? That is a good question.

[00:28:51]So if this was 36, that's 36. That's got to be 81. And that would be a four. And if this is 81, if this is 81, that would be 64, wouldn't it? I think.

[00:29:19]And that would be a three.

[00:29:22]So, we're always using 81 in one of those.

[00:29:26]Uh, is that true? Why couldn't it be?

[00:29:28]Oh, it couldn't be 16 here because that would break this digit. Yeah, that feels right then. So, yeah, where's one in the row? The answer is we don't know, but it can't be a 16 in anywhere. So, it's always going to be an 81. So, there is an eight in one of these two. So this final digit is not an eight.

[00:29:53]And if this is 81, we're left with threes, fours, and zeros. So it could be 64 or 36 there.

[00:30:05]Yeah. So it's still not clear actually.

[00:30:09]Or at least it's not clear clear to me.

[00:30:13]Um, what about if that's three or eight?

[00:30:23]Two and four in column in in this box have to be in these positions. It doesn't seem to Yeah. No, it does something. Um, because four is in these cells, it's not in these. And looking at my pencil marks, four is therefore in this domino, which means four we know has a nine at the end to it. It doesn't do anything. That's weird.

[00:30:48]Sorry, it doesn't do anything. I was hope I was hopeful for a moment, but it was fullon hope. Let's get rid of those sevens and hope Sedoku is going to come to our rescue.

[00:31:02]Although it's far it's far from clear to know where to look actually.

[00:31:11]Um, oh actually row four is restricted. Now there's a two. Uh, okay. This digit in the center of the row is three or eight.

[00:31:24]Oh, that's a 38 pair. That's good.

[00:31:27]Right. So yeah, the way I got that was looking at row four. I can see I've got a 1 six pair. So the other digits have to be from 2 38. This can't this sees a two in the middle. So that's three or eight. That's three or eight. So the digits that we've not put into this box are 156 into those cells. Whoops.

[00:31:48]Right. Right. Look at that. So that's a five. Now I've got a 156 in row six.

[00:31:56]Now this is the final digit. So that's got to be 8 2 3 or 1. That's a shame, isn't it?

[00:32:08]That's That is a shame.

[00:32:12]And in this in row six, it's 2 3 4 and 8 that are unplaced. So 2 3 4 8 into these cells. One of which is obviously the starting digit, but it I mean it works.

[00:32:27]That's going to be five, six, nine, or one.

[00:32:34]But it's nine.

[00:32:37]How has he come up with this? It's weird because now I've got a 156. I never noticed it. I've got a 156 triple in column four looking at that cell. So that's got to be nine, which means this has got to be four, which means I really hope it means something good.

[00:32:55]It means that that is four. Oh, that's right. That should do something for that pair there. Hopefully.

[00:33:06]Um, nine.

[00:33:12]Oh, it's trying hard for me, but it won't work in that. I was hoping I could do nine in box seven, but I don't think it's quite restricted enough.

[00:33:25]Okay.

[00:33:27]All right. So, let's check this out. The digits we've got left are 1 3 6 and 8 now.

[00:33:39]So, this can't be six because that can't be four and this can't be eight cuz 8 only goes with 81.

[00:33:53]So, is there something going on in column three there then with 1 2 3 6 8? No, it's not. Is there doesn't work?

[00:34:08]Unfortunately, I don't think there is anything. Let's try this column again.

[00:34:13]Nope.

[00:34:15]No, that doesn't work either. Um, okay.

[00:34:25]Two is in one of those two cells. That's just plain old Sudoku.

[00:34:30]That fairweathered friend.

[00:34:32]Um, this column we need 2 3 4 and 8.

[00:34:40]And so they've got 3 48 up here because we we worked out the two was down there.

[00:34:44]So 2 3 48 down here.

[00:34:48]This can't be four. So, this is three or eight. That does feel like it might be relevant, doesn't it? But it doesn't seem to do anything in the row.

[00:35:03]Bother. Um, okay.

[00:35:09]Okay. I don't know then. Um, I've got a horrible feeling I need to pencil mark box seven to within an inch of its life. I don't want to do that unless I absolutely have to. Is there some way I can maybe I can get a handle on the starting these two digits.

[00:35:34]But the problem is that no square, no two-digit square starts with 5, 9 or 7 anyway. So, the only thing I'm actually getting rid of here are the twos from this pencil mark, you know, of all the options that we could have, which which are Legion 1 3 4 6 and 8 I think are all in theory possible, which is very annoying indeed.

[00:36:11]How can we How can I do this?

[00:36:17]What is the trick?

[00:36:23]Is it Is it going to be Ah, okay. I've got something.

[00:36:29]Look at column four.

[00:36:35]Um, and if we ask where the five goes in column four, the answer is we don't know. as so often, but it seems to be in one of those two cells. Now, that means both of those are the ending points on squares. So, one of those digits is definitely a two to make a 25 square, which means this pencil mark is no longer valid. So, two in this box now is in one of two places.

[00:37:08]you sort of think that must help that what that means is but if this is a two this is a five if this is a two this is a five so one of those two cells is definitely a five I mean I don't think that's going to be helpful but it's a minor point I don't I don't see how to use it unfortunately okay let's pencil mark this this this little line then so this this digit I mean if we go through the it's 1 2 3 4 6 or 8 isn't it now what can we get rid of if anything we can get rid of six because it can't be 64 so it's 16 25 36 49 or 81 one now.

[00:38:12]That's That's absolutely bizarre.

[00:38:18]It's absolutely bizarre.

[00:38:21]Oh, no. That doesn't work. Oh, it nearly worked.

[00:38:25]Oh, that nearly worked. Oh, that's distressing. Um, I was realizing that the two there meant that one of those was a five. And then I was hopeful. I had a look down the column because that means one of these is a five. I thought maybe that would be really useful, but I actually don't think it does anything.

[00:38:44]That's so that's so upsetting.

[00:38:50]Um, okay.

[00:38:56]So, we need a new plan, Stan. Um, okay.

[00:39:05]Or Oh, we need to set ourselves free. How are we going to do it? Paul Simon, help me. Um, oh, nine. No, I was hopeful that Sedoku would come to our rescue. That can't be a four in the corner. Didn't see that. So, that's one, two, or three.

[00:39:28]What's this?

[00:39:31]16, 36, or 81?

[00:39:40]Is there some sedoku jigory pokery that we can avail ourselves of to to know the answer to any of these questions?

[00:39:53]Probably is somehow, but I don't know how.

[00:39:57]Um, nine.

[00:40:01]I do know nine is in one of those two. I think we've known that for some time.

[00:40:11]It's quite interesting. There's there's a lot of commonality. You know, if you scan along this row, if that couldn't be a four for some reason, you would have a 238 triple. And that would start to do things. Oh, look at that column. That column's got a lot of digits in it. So, the digits missing from this column are 1, 5, 6, 7.

[00:40:36]I'm going to have to do that, aren't I?

[00:40:38]1 5 6 7.

[00:40:41]That can't be seven. That can't be seven. Now, does that make any sense to anybody?

[00:40:49]No. Has done nothing.

[00:40:53]It's or it has almost done something in this row. There's sort of several cells that are fairly restricted.

[00:41:03]Couple of Oh, see it's nearly good there.

[00:41:07]If I knew somehow that wasn't a nine, we could do something.

[00:41:14]This is one of the most heavily pencil mark grids I think I've ever concocted on Cracking the Cryptic. I don't feel proud of myself for doing it this way, I have to say.

[00:41:27]Um, okay.

[00:41:35]So, I don't really know how to approach this to be honest.

[00:41:42]Here, here's a tiny point. Those two digits, whatever they are, they're from 56. If we ask where they go in this box, they've got to go there, don't they?

[00:41:53]That's the only places they can go.

[00:41:58]Now, does that help us in any in any way?

[00:42:06]So, that digit's got to be over here, but it could be there. I think this one six pair is that Oh, there's a 156 triple.

[00:42:20]Oh, yeah. There's there's lots of weird 156 triples and things.

[00:42:30]It might be that there's some way of disambiguating, you know, which which is 16 pairs and which are 36 pairs.

[00:42:42]This r that can't be a 16 pair. That's going to break that. So that can't begin with a one.

[00:42:54]So how can it end in a three?

[00:42:58]That's nons. That's a nonsense pencil mark.

[00:43:03]Right. Okay. So, that might do something. He said desperately. I don't think it has done anything. It's giving me a one six pair there.

[00:43:19]Um, has it done something in this column or is it It can't be these. It just can't be, can it?

[00:43:28]I well I'd be I'd be astonished which means it will be for some reason I can't concoct um okay let's let's think about that we know that the ending digits are ones have to go back to the list again four 5 6 and 9 now is anything taken out of these five is taken out by the pencil mark at the So that that's a lot of things going on there.

[00:44:03]That is a lot of things going on.

[00:44:06]But it's it's actually almost interesting.

[00:44:12]You know, if you look at that column, there's almost the possibility of something quite astounding going on.

[00:44:21]But it doesn't quite do it.

[00:44:26]Four, five, six, nine.

[00:44:29]So, eight.

[00:44:32]And so, two has to be in one of these positions.

[00:44:38]Oh, we worked out there was some weird point about two in column three having to be in one of those two positions, wasn't there?

[00:44:48]But that doesn't seem to have resolved everything that we need it to.

[00:44:54]And I mean literally I've pencil marked everything apart from the end of this line.

[00:44:59]So okay. So how are we going to make more progress here?

[00:45:08]Two can't end a square. So two is in one of these three.

[00:45:16]Sevens.

[00:45:21]No.

[00:45:25]Um, I am baffled. Count me amongst the baffled.

[00:45:31]I am baffled. There's a 238 triple here.

[00:45:34]I don't know whether this is meant to be a coloring puzzle at this point. It could be.

[00:45:41]Um, is there got this 56 here?

[00:45:53]So, I know one of these digits is two.

[00:45:58]One of those digits is eight as well to go with the one, which is almost good. I mean, it means this digit can't be an eight, but I'm not sure it. And the other digit there is going to be a one or a three.

[00:46:20]Um, but which of those I don't think I know.

[00:46:32]No, can't see it. Okay. So, we've got to try something else.

[00:46:41]I is there a reason that this could that be 36?

[00:46:50]Then these would be 148.

[00:46:56]I don't know. I do. I think I'm missing something obvious. Probably.

[00:47:02]But it's very hard to know where the grid has got very densely cluttered at this juncture.

[00:47:10]Um I mean it it couldn't be something.

[00:47:20]No, I don't know.

[00:47:24]What about Okay, I'm going to have to look at these digits and but I don't think there's any point. I really don't because I think we're in a situation where those can be 1 4 5 6 or nine apart. I suppose they can't be four.

[00:47:38]So what? Oh god. See how how am I meant to see that?

[00:47:44]So what that's telling me is look look at those in that box. That is a quadruple on 1 5 6 and 9.

[00:47:55]Which means the other digits in this box are are from 2 3 4 and 8. So this cell is two three or eight. Now I have said there's a two in one of those which seems reasonable looking at this box. So that's come. Oh, see look at this. Now I've got a 38 pair here. This is magic.

[00:48:15]So now I've got a 38 pair here. So those don't those aren't 38 anymore, right? So what has that done to the price of bread? Has that done anything really great?

[00:48:34]This is now one or two.

[00:48:37]So that's never one anymore because 81 has disappeared because of this 38 pair. So that's come down to five or six which doesn't do it. This lost the ability to be three or eight.

[00:48:56]So that loses its ability to be one.

[00:49:04]And hopefully he says this will all reveal something truly profound.

[00:49:14]What that is I don't know but I don't think it has okay but that okay clearly clearly there is something um you know that the importance of pencil marking quite dramatically was revealed there wasn't it.

[00:49:43]Although I don't think it's quite done enough for us, he says, desperately trying to spot something.

[00:49:55]You guys have probably already seen it and they're like shouting at me. Ah, I haven't got it yet. I'm so sorry if it is obvious.

[00:50:05]Um, do we think it's this? I don't think it is this row, but I I will check this digit out. Um, that sees a 38 pair and a two. So, it is a one, a four, a five, or a six. See? 7 8 9 1 4 5 6 Is that good?

[00:50:41]I mean, this is just a wash with So, this is why I should never do puzzles um in this manner. It does not suit my style. People always talk about having styles for Sudoku. Um, and I know a lot of people enjoy a a heavily pencil marked puzzle, but I find in this sort of situation, I find it completely baffling to look at. I have no idea where I should be devoting my time because it's just a completely overwhelming amount of information.

[00:51:14]Um but but we do not abandon our band of at ring puzzles. So I need to come up with something.

[00:51:26]What is that?

[00:51:31]Um I wish I knew. I really do.

[00:51:40]What do we think it could be?

[00:51:46]This 38 is the most exciting thing I've found recently.

[00:51:52]Is there a way to make better use of that?

[00:51:56]And 567.

[00:52:02]Um, one of these is 49, isn't it? We just don't know which one.

[00:52:15]So, if don't think that's easy to see.

[00:52:22]I mean, it might be, but it's not.

[00:52:26]It almost looks like row three is trying to be helpful, doesn't it, but I don't think that digits under any pressure.

[00:52:34]There's a 156 triple in that column.

[00:52:37]Maybe if I highlight triples as I see them. 156 there.

[00:52:45]Is there anything else triply that we can use? Um 1 4 5 69 is almost is almost possible in that column.

[00:53:01]Oh, where's eight? No, no, that Oh, yeah, that's that's actually there is a small point there. Where's eight in this column? And the answer, as so often, is I don't know. But it's one of those two, which takes eight out of this one, which takes one out of this one, which means that's good. Good grief. It can't be that, can it? That see what? See, see what that's done. That's given me a five six pair here, which makes this a one, which makes this an eight now. So that's not an eight, which means this is not a one. That's This is huge.

[00:53:38]So this is a uh see it's a six but we don't still don't know what the digits above it is. But we can get rid of sixes down there. This now becomes a one. So that becomes an eight.

[00:53:49]Oh well this is no this is very this is very encouraging. So that becomes a three and that's got to be a six. So this becomes a one. So this becomes an eight. That becomes a three and that becomes a six. It's actually doing things.

[00:54:06]Whether it's doing enough things or not is moot.

[00:54:10]But hopefully this now is not a one. So that's a five six pair. This being a three. Oh, that three is lovely. So that's two, that's three, that's six, that's six, that's five, that's two. By mathematics, this is now eight. So that's three.

[00:54:32]That's two. This is eight. So the middle three rows somehow or other are actually finished. There's a 159 triple there.

[00:54:42]Um okay.

[00:54:47]So we can take six out of this cell.

[00:54:49]Look, there's a 1 four five. What's the Oh, this can't be five anymore because that can't be two. So the five gets placed in this box. Box seven.

[00:55:02]That can't be two anymore.

[00:55:06]2 48 there.

[00:55:09]1 4 1 4 69 in that box. That's a surprise. Look at those. So, this can't be 1 or four. That's got to be three and eight. Three we know will go with six.

[00:55:20]Eight we know will go with one. So, those are not four and nine.

[00:55:26]So, this is a one six pair. So that's a nine and that's a four and that works.

[00:55:31]So that's good. Um that puts nine in the corner down here which makes this four.

[00:55:39]Come on now. Is that going to be very good?

[00:55:44]Well, one six here takes one out of it makes that five. So that's two.

[00:55:51]Okay.

[00:55:53]There's a 134 triple there.

[00:55:57]Yeah. Okay. And we've got a a sort of hick nine pair as well at the top. But there's lo there's loads of pencil mark reductions we can do. Now there's a 38 pair in the top row out of nowhere.

[00:56:16]Um this one six makes this a nine at the top. So that's going to go with four.

[00:56:20]That's going to be three. That's going to be six. So that's a one. That was a 16 after all this time. Uh this is a five. So that's a two.

[00:56:30]Take five and two out of there. That becomes 3 eight. Which means this is two. This is five. This is one. This is eight. The fact that it's actually working it makes me think that we might be on the right lines. But I have to say I think I think it's very possible that there was a better way of attempting this puzzle. So, the way I've done it, I I I feel is is not in my best. It wasn't in my best interests, if you see what I mean. I should have probably just been calm and accepted, you know, that it might I wasn't really going to get anywhere and just waited for a moment. Look at this. It's all filling in. It really is. It's all filling in. It is all filling in genuinely. Yeah, I think I should have Oh, that's can't be a four in that cell.

[00:57:28]I don't like that. That looks wrong from a Sudoku three.

[00:57:32]Um, it's brilliant. I mean, it's a baffling puzzle to be honest that that's that it's one of these ones that's been heuned out of the rocks of nature because it's um it just exists, doesn't it? the there's this thing, but apart from that, it's utterly symmetrical.

[00:57:57]I mean, it's got a three cell prime in the middle and a given digit, I suppose.

[00:58:01]And yet somehow that allows it to all be unwound.

[00:58:06]And you had I had to be very careful.

[00:58:08]There was something I did here which knocked a digit out of that one. And then suddenly it just all fell, didn't it, after that? It's very very clever art. I don't know how you have these ideas, let alone execute them with that sort of a plum. And yet you do week after week, year after year. The man is a total revelation. Wonderful puzzle.

[00:58:30]Let me know in the comments how you got on. Let me know if you found um a better way of approaching it than I did. Be interested to know. And we'll be back later with another edition of Cracking the Cryptic.

[00:58:41]Went downstairs and realized I don't think I pressed um tick on the machine.

[00:58:46]So, uh, yeah, it was what what a wally. Never mind. See, see you again later. Bye now.